Determining the position of an object in motion on a $3D$ plane

Question

Expressed as $x,y,z...$

$P_1 = (0,0,0)$

$P_2 = (1000,2000,3000)$

I know the formula for distance:  $$d=\sqrt{(x_2 - x_1)^2 + (y_2- y_1)^2 + (z_2- z_1)^2}$$

How do I find out where the object is halfway through its flight?

I'm using mysql, so geometric solutions may be possible using lines.

Read here for more info: https://stackoverflow.com/questions/54860047/mysql-determining-the-position-of-an-object-in-motion

Answer 1

The midway $M$ point between $P=(x_1,y_1,z_1)$ and $Q=(x_2,y_2,z_2)$ is given by $$ M=\Big(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2} \Big). $$

EDIT:

What is happening here is actually you calculate $$ (x_1,y_1,z_1)+t\big((x_2,y_2,z_2)- (x_1,y_1,z_1)\big) $$

where we chose $t=\frac{1}{2}$ above, you could pick anything you like.

EDIT:

Coordinates are given by

$$ \Big((1-t)x_1+tx_2,(1-t)y_1+ty_2,(1-t)z_1+tz_2 \Big) $$